Not what the law is, or what hate crimes are.
Lying about basic shit wastes everyone's time. And I don't believe for one second you're actually confused about the basic facts, here.
And motive. Mens rea is a broad concept, it refers to intent and motive both, as well as your understanding of the facts at hand. It's about what you were thinking when you did the act in question.
It's why "not guilty by reason of insanity" is a valid plea; you may have torn someone's throat out with your teeth, but if you were having a psychotic break, there's no mens rea. You may still need to be hospitalized, for the protection of yourself and others, but you're not guilty of a crime, even if there's no question that you tore that innocent person's throat out.
Given that the latter is often grounds for reducing a charge from first degree murder to second, and if you walked in on him having sex with your wife, potentially right down to voluntary manslaughter, that's an obvious "yes".Should the law care whether that intent was "because he was black" more than "he slept with my wife"?
Yes, the law cares about mens rea. Not just actus reus. Saying it should focus exclusively on the act, and not the intent and motive, is to throw out hundreds of years of legal jurisprudence and the entire basis of Western law, in all its variations.